Four masses are fixed on a massless rod as shown in the figure. The moment of inertia about the axis $PQ$ is about ........ $kg-m^2.$

During the mean life of a radioactive element,the fraction that disintegrates is

Two sources $A$ and $B$ are sending notes of frequency $680 \, Hz$. A listener moves from $A$ towards $B$ with a constant velocity $u$. If the speed of sound in air is $340 \, ms^{-1}$, what must be the value of $u$ so that the listener hears $10$ beats per second (in $ \, ms^{-1}$)?

$\frac{1}{2 \cdot 3} + \frac{1}{4 \cdot 5} + \frac{1}{6 \cdot 7} + \frac{1}{8 \cdot 9} + \dots$ is equal to

$A$ prism of refractive index $\sqrt{2}$ has a refracting angle of $60^{\circ}$. In order for a ray to suffer minimum deviation,it should be incident at an angle of.......$^{\circ}$.

Two spheres $A$ and $B$ are kept very near to each other. $A$ is negatively charged and $B$ is earthed. The true statements are:
$(A)$ Charge on $B$ is zero
$(B)$ Potential at $B$ is zero
$(C)$ Charge is uniformly distributed on $A$
$(D)$ Charge is non-uniformly distributed on $A$